1. Using the Basic Kinematic Equation generates complicated expressions for different types of accelerations when considering motion from the point of view of a rotating frame. What motivates us to use this complex form of the expression for acceleration?
2. The precise form of Newton's 2nd Law is F=dp/dt, where p=mv and when differentiation is done with respect to an inertial frame. For a constant mass system, the Law can be simplified to F=ma. What is the simplified form of the Law for a system with varying mass and constant velocity?
3. Classify each of the following with one of the choices provided [note that the apostrophe, ', denote a derivative wrt time]:
a. a = dv/dt [a kinematic relationship] vs [a dynamic relationship]
b. F = ma [a kinematic relationship] vs [a dynamic relationship]
c. T = Iw' [a kinematic relationship] vs [a dynamic relationship]
d. x = r*cos(theta) [a kinematic relationship] vs [a dynamic relationship]
e. mx'' + bx' + kx = F(t) [linear equation] vs [nonlinear equation]
f. Ri+Li'=V(t) [time invariant equation] vs [time-varying equation]
g. A 2nd order response with overshoot [overdamped response] vs [underdamped response]
h. A 1st order system response [sinusoidal] vs [exponential]
in the above equations, a is acceleration, v is velocity, t is time, F is force, m is mass, T is torque, I is inertia, w is angular velocity, b is damping coefficient, k is spring constant, x is position, R is resistance, i is current, L is inductance, r is magnitude of a position vector, theta is the angle of a position vector, and V is voltage.
5. A lever has a fulcrum placed 2/3 of the way down its length. What is the mechanical advantage if a load at the short end is lifted by an effort at the long end?
6. What are the two primary motivations for using closed loop (feedback) control rather than simple open loop control?
7. What does the acronym PID stand for? Explain the control strategy implied by each term in this acronym. Also explain why each strategy is potentially a good strategy and when they may be most appropriate.
8. Consider 3 types of spacecraft mechanisms: deployment mechanisms, communication antenna pointing mechanisms, and telescope mirror pointing devices. Rank these three in terms of typical required accuracy (e.g., list them from most accurate to least accurate).
9. A dc motor operating at 12V has a max torque of 6 units of torque and a max angular velocity of 1200 rpm. The desired operating point is 500 rpm and 2 units of torque.
a. determine Kt/R for the motor given the max numbers
b. determine Kemf for the motor given the max numbers
c. determine the voltage to be used for the desired operating point
d. when operating at the standard 12V level, if a 3:1 gearbox is used in order to increase torque, what is the max torque coming out of the gearbox, and what is the max shaft speed coming out of the gearbox?
10. [THIS QUESTION WON'T BE GRADED]Define accuracy, resolution and repeatability given the descriptions provided by Dr. Clark in his mechanisms lecture. (as defined in Dr. Clark's lecture).